Polygon model generating apparatus, polygon model generation method, and program

ABSTRACT

A polygon model generating apparatus, a polygon model generation method, and a program each capable of highly precisely generate a polygon model whose surface is set along the contour of a group of points, are provided. An initial polygon model generating part (72) generates a polygon model that includes plural polygons on the basis of point group data indicating the group of points in a virtual space. An intersectional polygon deleting part (82) identifies an intersectional polygon that is the polygon intersecting with a line whose both ends are a first position to view therefrom the polygon model in a virtual space and a second position that is the position of a point belonging to the group of points. An intersectional polygon deleting part (82) deletes the intersectional polygon from the polygon model.

TECHNICAL FIELD

The present invention relates to a polygon model generating apparatus, apolygon model generation method, and a program.

BACKGROUND ART

A technique of generating a polygon model positioned along a contour ofa group of points is present. As an example of this technique, PTL 1describes a technique of generating a polygon model arranged in avirtual space from an image that includes depth information obtained byshooting an object arranged in the real space.

With this technique, an initial sculpture including triangular polygonsis first generated in the virtual space. A point in the virtual space (adata point) correlated with a combination of each of the pixels in theobtained image and a depth of the pixel is thereafter identified.Ray-casting is thereafter executed from the origin to the identifieddata point and an intersection of the ray-casted ray and the polygon isidentified. A vertex of the polygon is thereafter moved in accordancewith a length between the identified intersection and the data point andthe initial sculpture is thereby deformed.

CITATION LIST Patent Literature

[PTL 1]

PCT Patent Publication No. WO2015/193708

SUMMARY Technical Problem

The inventors discuss a new approach of generating a polygon model setalong a contour of a group or points. With this approach, point groupdata it a group of points in a virtual space is first generated from animage including depth information, and the like. Delaunay triangulation(tetrahedralization) using, for example, a point belonging to the groupof points as the Delaunay point, or the like is thereafter executed andthereby a polygon model including plural polygons whose vertexes areeach a point belonging to the group of points.

The polygon model generated as above is however not a polygon modelwhose outer surface is set along the contour of the group of points.Concerning this, it can be considered that the polygon model can be setto be closer to the polygon model whose outer surface is set along thecontour of the group of points by, for example, deleting the polygonseach including a side that is longer than a predetermined length, fromthe polygon model. Even when this deletion is executed, however, anysufficiently precise polygon model whose contour is set along thecontour of the group of points may not be obtained due to an influenceof the uneven density of the group of points, and the like.

The present invention was conceived in view of the above problem and anobject thereof is to provide a polygon model generating apparatus, apolygon model generation method, and a program that each can highlyprecisely generate a polygon model that is set along the contour of agroup of points.

Solution to Problem

To solve the above problem, the polygon model generating apparatusaccording to the present invention includes a polygon model generatingpart that generates a polygon model including plural polygons on thebasis of point group data that indicates a group of points in a virtualspace, an intersectional polygon identifying part that identifies anintersectional polygon that is the polygon intersecting with a linewhose both ends are a first position to view therefrom the polygon modelin the virtual space and a second position that is the position of apoint belonging to the group of points, and an intersectional polygondeleting part that deletes the intersectional polygon from the polygonmodel.

An aspect of the present invention further includes an image obtainingpart that obtains an image obtained by shooting an object to be shot bya real camera in a real space, a point group data generating part thatgenerates the point group data for which the points belonging theretoeach correspond to a point on the object to be shot in the real space,on the basis of the image, and a corresponding camera positionidentifying part that identifies the position in the virtual spacecorresponding to the position in the real space, of the real camera at atime when the object to be shot is shot. The intersectional polygonidentifying part identifies the intersectional polygon using theposition identified in accordance with the corresponding camera positionidentification procedure, as the first position.

Moreover, an aspect of the present invention further includes aninvisible polygon identifying part that identifies an invisible polygonthat is the polygon invisible by any of one or plural virtual camerasset in the virtual space, and an invisible polygon deleting part thatdeletes the invisible polygon from the polygon model.

Moreover, an aspect of the present invention further includes a pointdensity value, determining part that determines the value of the pointdensity correlated with a point belonging to the group of points on thebasis of a distribution of the group of points, and a long-side polygondeleting part that, in the case where the length of a side constitutingthe polygon exceeds a threshold value in accordance with the value ofthe point density correlated with an end point of the side, deletes thepolygon from the polygon model.

In this aspect, for only each of at least some of the points whosevalues of the point density correlated thereto are each greater than apredetermined value, the intersectional polygon identifying part mayidentify the intersectional polygon using the position of the point asthe second position.

Moreover, a polygon model generation method according to the presentinvention includes a polygon model generation step of generating apolygon model that includes plural polygons on the basis of point groupdata indicating a group of points in a virtual space, an intersectionalpolygon identification step of identifying an intersectional polygonthat is the polygon intersecting with a line whose both ends are a firstposition to view therefrom the polygon model in the virtual space and asecond position that is the position of a point belonging to the groupof points, and an intersectional polygon deletion step of deleting theintersectional polygon from the polygon model.

Moreover, a program according to the present invention causes a computerto execute a polygon model generation procedure of generating a polygonmodel that includes plural polygons on the basis of point group dataindicating a group of points in a virtual space, an intersectionalpolygon identification procedure of identifying an intersectionalpolygon that is the polygon intersecting with a line whose both ends area first position to view therefrom the polygon model in the virtualspace and a second position that is the position of a point belonging tothe group of points, and an intersectional polygon deletion procedure ofdeleting the intersectional polygon from the polygon model.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a configuration diagram of a polygon model generatingapparatus according to an embodiment of the present invention.

FIG. 2 is a diagram schematically depicting an example of the statewhere an object to be shot is arranged in a real space.

FIG. 3 is a diagram, schematically depicting an example of the statewhere a polygon model copying the object to be shot is arranged in avirtual space.

FIG. 4 is a diagram schematically depicting an example of plural pointsthat belong to ca group of points indicated by point group data.

FIG. 5 is a diagram depicting an example of point data.

FIG. 6 is a diagram schematically depicting an example of the statewhere an initial polygon model is arranged in the virtual space.

FIG. 7 is a diagram depicting an example of polygon data.

FIG. 8 is an explanatory diagram explaining an example of a long-sidepolygon deletion process.

FIG. 9 is an explanatory diagram explaining an example of anintersectional polygon deletion process.

FIG. 10 is a diagram schematically depicting an example of the statewhere an intermediate polygon model is arranged in the virtual space.

FIG. 11 is a diagram depicting an example of a virtual space image.

FIG. 12A is an explanatory diagram explaining an example of a normalline direction correction process.

FIG. 12B is an explanatory diagram explaining an example of the normalline direction correction process.

FIG. 13 is a functional block diagram depicting an example of thefunctions implemented in a polygon model generating apparatus accordingto an embodiment of the present invention.

FIG. 14 is a flowchart depicting an example of the flow of processesexecuted by the polygon model generating apparatus according to anembodiment of the present invention.

FIG. 15 is a flowchart depicting an example of the flow of processesexecuted by the polygon model generating apparatus according to anembodiment of the present invention.

FIG. 16 is a flowchart depicting an example of the flow of processesexecuted by the polygon model generating apparatus according to anembodiment of the present invention.

FIG. 17 is a flowchart depicting an example of the flow of processesexecuted by the polygon model generating apparatus according to anembodiment of the present invention.

DESCRIPTION OF EMBODIMENT

An embodiment of the present invention will be described below in detailwith reference to the drawings.

FIG. 1 is a configuration diagram of a polygon model generatingapparatus 10 according to an embodiment of the present invention. Thepolygon model generating apparatus 10 according to the presentembodiment is a computer such as, for example, a game console or apersonal computer. As depicted in FIG. 1, the polygon model generatingapparatus 10 according to the present embodiment includes, for example,a processor 12, a storing part 14, an operation part 16, and adisplaying part 18.

The processor 12 is a program control device such as, for example, acentral processing unit (CPU) that operates in accordance with programsinstalled in the polygon model generating apparatus 10. The processor 12according to the present embodiment also includes a graphics processingunit (GPU) that draws an image in a frame buffer on the basis of agraphics command and data supplied from the CPU.

The storing part 14 is a storage element such as a read-only memory(ROM) or a random access memory (RAM), or a hard disc drive. The storingpart 14 stores therein programs to be executed by the processor 12, andthe like. Moreover, the storing part 11 according to the presentembodiment has an area for the frame buffer secured therein in which theimage is drawn by the GPU.

The operation part 16 is a user interface such as a keyboard, a mouse, acontroller of a game console, accepts an operational input by the user,and outputs a signal indicating the content of the operational input tothe processor 12.

The displaying part 18 is a displaying device such as a liquid crystaldisplay and displays thereon various types of image in accordance withthe instruction of the processor 12.

In addition, the polygon model generating apparatus 10 may include acommunication interface such as a network board, an optical disc drivethat reads optical discs such as a digital versatile disc (DVD)-ROM anda Blu-ray (registered trademark) disc, a universal serial bus (USB)port, and the like.

FIG. 2 is a diagram schematically depicting an example of the statewhere an object 20 to be shot is arranged in a real space 22 accordingto the present embodiment. FIG. 2 depicts a real object having a shapelike that of Stanford Sunny as an example of the object 20 to be shot.

FIG. 3 as a diagram schematically depicting an example of the statewhere a polygon model copying the object 20 to be shot is arranged in avirtual space 32. In the polygon model generating apparatus 10 accordingto the present embodiment, the polygon model depicted in FIG. 3 isfinally generated on the basis of, for example, one or plural shotimages each obtained by shooting the object 20 to be shot that isexemplified in FIG. 2 by a real camera 24 arranged in the real space 22.The finally generated polygon model will hereinafter be referred to as“final polygon model 30.”

The final polygon model 30 depicted in FIG. 3 is constituted by pluralpolygons 34. The virtual space 32 according to the present embodiment isa space formed by modeling the real space 22. In the present embodiment,the position and the orientation of the object 20 to be shot in the realspace 22 are reflected on the position and the orientation of the finalpolygon model 30 in the virtual space 32. Hereinafter, the position inthe real space 22 will be represented using an X1-Y1-Z1 coordinatesystem and the position in the virtual space 32 will be representedusing an X2-Y2-Z2 coordinate system.

A generation process for the final polygon model 30 on the basis of theobject 20 to be shot and executed by the polygon model generatingapparatus 10 will be described below.

The polygon model generating apparatus 10 according to the presentembodiment first obtains one or plural shot images obtained by shootingthe object 20 to be shot by the real camera 24. In addition, the shotimages may simultaneously be shot by the plural real cameras 24 or theshot images of the object 20 to be shot may be shot from variousdirections by one real camera 24. The real camera 24 may be a cameracapable of shooting a shot image that includes the depth informationsuch as a stereo camera or a camera with an infrared ray distancesensor. In this case, for example, a depth image that shows thedistribution of the distance from the real camera 24 to the object 20 tobe shot, that is correlated with each of the pixels included in the shotimage, may be generated together with the shot image by the real camera24.

FIG. 4 is a diagram schematically depicting an example of plural points36 that belong to the group of points indicated by the point group datagenerated on the basis of the one or plural shot images. In the presentembodiment, the point group data indicating the group of points to whichthe plural points 36 in the virtual space 32 belong, is generated usinga known approach on the basis of the one or plural shot images obtainedby the polygon model generating apparatus 10. Moreover, the point groupdata may be generated on the basis of the shot images and the depthimage.

In the present embodiment, in the case where the plural shot images areshot, unevenness may be generated in the density of the points 36belonging to the group of points due to the difference in the distancebetween the object 20 to be shot and the real camera 24 and thedifference in the resolution among the plural real cameras 24 that shootthe shot images for the time when the shot images are shot. Moreover,unevenness may be generated in the density of the points 36 belonging tothe group of points also due to the orientation of the object 20 to beshot to the real cameras 24.

FIG. 5 is a diagram depicting an example of the point data included inthe point group data and correlated with one of the points 36. The pointdata depicted in FIG. 5 includes a combination of a point identification(ID) that is identification information of the point 36 correlated withthe point data, and coordinate data that indicates the three-dimensionalcoordinate values representing the position of the point 36 representedin the X2-Y2-Z2 coordinate system. The point group data generated in thepresent embodiment includes pieces of the point data exemplified in FIG.5 for the number corresponding to the number of the points 36 belongingto the group of points.

The positions of the points 36 depicted in FIG. 4 are thereaftercorrelated with the positions of the points on the surface of the object20 to be shot that are identified on the basis of the one or the pluralshot images. In the present embodiment, for example, the coordinatevalues (x1, y1, z1) in the X1-Y1-Z1 coordinate system in the real space22 are thereafter mapped to the coordinate values (t·x1, t·y1, t·z1) (tis a constant) in the X2-Y2-Z2 coordinate system in the virtual space32. In the embodiment, the shape of a three-dimensional body whosesurface is set along the contour of the group of points depicted in FIG.4 is therefore substantially same as the shape of the object 20 to beshot depicted in FIG. 2.

The polygon model generating apparatus 10 according to the presentembodiment thereafter generates polygon model data that indicates thepolygon model constituted by the plural polygon on the of the points 36belonging to the group of points depicted in FIG. 4. In this case, it isassumed, for example, that the polygon model data is generated thatindicates the polygon model exemplified in FIG. 6 constituted by thepolygons 34 vertexes are the points 36 belonging to the group of pointsdepicted in FIG. 4. In addition, some of the points 36 belonging to thegroup of points may not each be any vertex of the polygons 34 but mayeach be a point on the face of any one of the polygons 34. The polygonmodel depicted in FIG. 6 will hereinafter be referred to as “initialpolygon model 40.” The initial polygon model 40 constituted by pluraltriangles may be generated by executing Delaunay triangulation(tetrahedralization) using, for example, the point 36 belonging to thegroup of points depicted in FIG. 4 as the Delaunay point. In addition,the initial polygon model 40 does not need to be generated by theDelaunay triangulation and no problem arises when the initial polygonmodel 40 is generated using another method.

FIG. 7 is a diagram depicting an example of the polygon data that iscorrelated with one of the polygons 34. In the present embodiment, thepolygon model data is generated that includes the pieces of polygon datafor the number corresponding to the number of the polygons 34 includedin the initial polygon model 40. The polygon data includes, for example,a polygon ID that is the distinguishing information for the polygon 34correlated with the polygon data and vertex data that is a list withorder of the point IDs of the points 36 that are the vertex of thepolygon 34.

Moreover, a normal line direction (the front and the back) of thepolygon 34 correlated with the polygon data by the polygon data may bedefined. For example, this is the order of the vertexes to be thecounterclockwise direction when the polygon 34 is seen from its frontside. The list with order of the points 36 respectively correlated withthe vertexes may be included in the polygon data as vertex data. In thiscase, the direction from the back side of the polygon 34 toward thefront side thereof may be defined as the normal line direction.

In addition, the data structure of the polygon data is not limited tothe one depicted in FIG. 7.

Concerning the above, the initial polygon model 40 exemplified in FIG. 6includes a convex hull of the group of points depleted in FIG. 4 and itcannot be stated that the surface thereof is set along the contour ofthe group of points depicted in FIG. 4. In the present embodiment, thepolygons 34 constituting the initial polygon model 40 exemplified inFIG. 6 are sequentially deleted by executing a long-side polygondeletion process, an intersectional polygon deletion process, and aninvisible polygon deletion process that will be described below.According to the present embodiment, the initial polygon model 40exemplified in FIG. 5 is brought close to a polygon model whose surfaceis set along the contour of the group of points depicted in FIG. 4, thatis, a polygon model whose reproduction precision for the object 20 to beshot is high, by executing as above.

Concerning the above, an example of the long-side polygon deletionprocess will be described with reference to FIG. 8.

In the long-side polygon deletion, process, the value of the pointdensity is first determined that is correlated with each of the points36 belonging to the group of points, on the basis of the distribution ofthe group of points depleted in FIG. 4.

Concerning the above, the number of the points 36 included in anoctahedron having a predetermined volume and centering the specificpoint 36 may be determined as the value of the point density thatcorresponds to the specific point 36.

Moreover, the point group data may include data having an octree datastructure that correlates the position of each of the points 36 arrangedin the virtual space 32 with one of partial spaces formed by recursivelydividing into eight a three-dimensional space occupied by a cube whosesurface covers the group of points indicated by the point group data. Inthis case, the density of the points 36 roughly identified on the basisof the octree may be determined as the value of the point densitycorrelated with the point 36. The value of the point density isdetermined at a high speed by executing as above.

In addition, the determination method for the value of the point densityis not limited to the above method.

For each of sides 42 included in the initial polygon model 40, athreshold value is next determined that is correlated with the side 42on the basis of the value of the point density correlated with the point36 that is an end point of the side 42. In the example in FIG. 8, it isassumed that the value of the point density correlated with a point 36 athat is one end point of a side 42 a is identified as v1. It is alsoassumed that the value of the point density correlated with a point 36 bthat is the other end point of the side 42 a is identified as v2. Inthis case, a threshold value th is determined that is correlated withthe side 42 a on the basis of, for example, the value v1 and the valuev2. Concerning this, for example, a threshold value correlated with asmaller value of the value v1 and the value v2 may be determined to bethe threshold value th. Moreover, for example, a threshold value,correlated with as greater value, of the value v1 and the value v2 mayalso be determined to be the threshold value th. Moreover, for example,a threshold value correlated with the average of the value v1 and thevalue v2 may also be determined to be the threshold value th.

In addition, it is assumed in the present embodiment that the rule forthe correlation between the value of the point density and the thresholdvalue is provided in advance and the threshold value can be determinedon the basis of the value of the point density. Moreover, it is alsoassumed therein that a smaller value is determined as the thresholdvalue to be correlated with the value of the point density as the valueof the point density is greater.

The sides 42 for each of which the length of the side 42 is larger thanthe threshold value that is correlated with the side 42 are thereafteridentified from the sides 42 included in the initial polygon model 40.The polygons 34 including the identified sides 42 are thereafter deletedfrom the initial polygon model 40. In other words, the pieces of polygondata corresponding to the polygons 34 including the identified sides 42are deleted from the polygon model data. In the example in FIG. 8, inthe case where a length L of the side 42 a exceeds the threshold valueth, a polygon 31 a and a polygon 34 b each including the side 42 a aredeleted from the initial polygon model 40.

When the polygons 34 each including the side 42 that is longer than apredetermined length are uniformly deleted from the initial polygonmodel 40 exemplified in FIG. 6 without executing the long-side polygondeletion process described above, no highly precise polygon model may beobtained due, to the influence, of the unevenness of the density of thegroup of points depicted in FIG. 4. For example, when the predeterminedlength described above is reduced, the surface of the polygon model isset along the contour of the group of points even at recessed portionswhole the possibility for the polygon model to have holes formed thereonis increased. Moreover, when the predetermined length described above isincreased, the possibility for the polygon model to have holes formedthereon is reduced while, the possibility for the surface of the polygonmodel not to be set along the contour of the group of points in therecessed portions is increased.

In the long-side polygon deletion process according to the presentembodiment, the polygons 34 each including a long side are deleted onthe basis of a threshold value on with the density of the points 36belonging to the group of points is reflected. More specifically, forexample, in the portion whose, points 36 are dense, even the polygons 34each including a relatively short side are deleted while, in the portionwhose points 36 are sparse, even the polygons 34 each including arelatively long side are not deleted. In this manner, in the presentembodiment, a highly precise polygon model can be obtained.

In the present embodiment, the intersectional polygon deletion processdescribed below is thereafter executed to further improve the precisionof the polygon model, Concerning the above, an example, of theintersectional polygon deletion process will be, described withreference to FIG. 9.

In the intersectional polygon deletion process, the position in thevirtual space 32 is first identified that corresponds to the position ofthe real camera 24 in the real space 22 for the time when the shot imageis shot. In the case where the X1-Y1-Z1 coordinate values of theposition of the real camera 24 are (x1, y1, z1) as above, (t·x1, t·y1,t·z1) are identified as the X2-Y2-Z2 coordinate values of the positionin the virtual space 32 that corresponds to the position of the realcamera 24. The position in the virtual space 32 that corresponds to theposition of the real camera 24 in the real space 22 identified as abovewill hereinafter be referred to as “corresponding camera position of thereal camera 24.”

The point 36 in the virtual space 32 that corresponds to a point on thesurface of the object 20 to be shot correlated with a pixel including inthe shot image shot by the real camera 24 is thereafter identified. Thepoint 36 identified as above will hereinafter be referred to as “visiblepoint of the real camera 24.”

Ray-casting is thereafter executed from the corresponding cameraposition of the real camera 24 to each of the points 36 for each ofwhich the value of the point density correlated thereto is greater thana predetermined value, of the visible points of the real camera 24.

The polygons 34 intersecting with the rays of the ray-casting aredeleted from the polygon model. For example, it is assumed that, whenthe ray-casting is executed from a corresponding camera position P1 ofthe real camera 24 to a point 36 c that is a visible point of the realcamera 24 depicted in FIG. 9, a ray of the ray-casting and a polygon 34c intersect with each other at a position P2. In other words, it isassumed that the polygon 34 c is identified as the polygon 34 thatintersects with a line whose both ends are the corresponding cameraposition P1 and the position of the point 36 c. In this case, thepolygon 34 c is deleted from the polygon model. In other words, thepolygon data corresponding to the polygon 34 c is deleted from thepolygon model data.

According to the intersectional polygon deletion process describedabove, the polygons 34 unable to be deleted in the long-side polygondeletion process can be deleted and the polygon model after theintersectional polygon deletion process is executed therefor is broughtcloser to the polygon model whose surface is set along the contour ofthe group of points.

The polygons 34 on the side more internal than the outer surface of thepolygon model may however remain even when the tong side polygondeletion process and the intersectional polygon deletion process asabove are executed. These polygons 34 do not contribute to theexpression of the outer appearance of the polygon model. It cantherefore be stated that the pieces of polygon data corresponding tothese polygons 34 are useless in the polygon model data.

The present embodiment is therefore adapted to delete the polygons 34 onthe side more internal than the outer surface of the polygon model bythe invisible polygon deletion process described below and, as a result,to reduce any useless portion of the data size of the polygon modeldata. Concerning this, an example of the invisible polygon deletionprocess will be described with reference to FIG. 10 to FIG. 12B.

As depicted in FIG. 10, the polygon model for which the long-sidepolygon deletion process and the intersectional polygon deletion processare already executed is arranged in the virtual space 32. The polygonmodel for which the lone side polygon deletion process and theintersectional polygon deletion process are already executed willhereinafter be referred to as “intermediate polygon model 50.” The outerappearance of the intermediate polygon model 50 is same as that of thefinal polygon model 30 while the intermediate polygon model 50 has thepolygons 34 on the side more internal than the outer surface remainingthereon as above. Concerning this, the polygons 34 included in theintermediate polygon model 50 may be arranged in the virtual space 32 inthe state where these polygons 34 can each be distinguished from eachother. For example, visible attributes such as the texture and the colorto be correlated with the polygon ID of each of the polygons 34 may beset for the polygon 34.

A virtual space image 54 exemplified in FIG. 11 is thereafter rendered,that shows the state where viewing is executed from virtual cameras 52arranged at positions in the virtual space 32 to view therefrom theintermediate polygon model 50, toward the intermediate polygon model 50.FIG. 11 depicts the virtual space image 54 that shows the state whereviewing is executed from the virtual camera 52 arranged at a position P3in FIG. 10 toward the intermediate polygon model 50. Concerning this,the visible attributes set for the polygon 34 may be reflected on thevirtual space image. The polygon 34 visible from the position from whichthe virtual space image 54 is shot (a visible polygon 34 d) isidentified. Concerning this, for example, the polygon 34 correspondingto the polygon ID correlated with the visible attributes set for thepolygon 34 whose image is included in the virtual space image 54 may beidentified as the visible polygon 34 d.

Concerning the above, as depicted in FIG. 10, for each of the pluralpositions in the virtual space 32, the arrangement of the virtual camera52, the generation of the virtual space image 54, and the identificationof the visible polygon 34 d that are described above may sequentially beexecuted. Moreover, the arrangement of the virtual camera 52, thegeneration of the virtual space image 54, and the identification of thevisible polygon 34 d may be executed in parallel processing at each ofthe plural positions in the virtual space 32. The polygon 34 notidentified as the visible polygon 34 d in any of the virtual spaceimages 54 is thereafter identified as an invisible polygon.

Concerning the above, for example, a visible polygon ID list that isempty in the initial state may be adapted to have the polygon ID of thepolygon 34 identified as the visible polygon 34 d added thereto. Thepolygon 34 whose, polygon ID is not included in the visible polygon IDlist may thereafter be identified as an invisible polygon.

The polygon 34 identified as the invisible polygon is thereafter deletedfrom the intermediate polygon model 50. In other words, the polygon datacorresponding to the invisible polygon is deleted from the polygon modeldata.

Moreover, in the present embodiment, in the invisible polygon deletionprocess, a normal line direction correction process is executed for thepolygon 34 identified as the visible polygon 34 d in each of the virtualspace, images 54.

In this case, for example, as depicted in FIG. 12A, in the case where,the normal line direction of the visible polygon 34 d is not directed tothe virtual camera 52, a normal line inversion count value correlatedwith the visible polygon 34 d is increased by one. In other words, inthe case where the inner product of a vector V1 in the direction of theshooting by the virtual camera 52 and a vector V2 in the normal linedirection of the visible polygon 34 d is positive, the normal line inout value correlated with the visible polygon 34 d is increased by one.

In contrast, for example, as depicted in FIG. 12B, in the case where thenormal line direction of the visible polygon 34 d is directed to thevirtual camera 52, the normal line inversion count value correlated withthe visible polygon 34 d is reduced by one. In other words, in the casewhere the inner product of the vector V1 in the direction of theshooting by the virtual camera 52 and the vector V2 in the normal linedirection of the visible polygon 34 d is negative, the normal lineinversion count value correlated with the visible, polygon 34 d isreduced by one. For this, it is assumed that the initial value of thenormal line, inversion count value correlated with the visible polygon34 d is zero.

As a result of the increasing or reducing of the normal line inversioncount value for each of all the virtual space images, the visiblepolygon 34 d whose normal line in count value correlated thereto ispositive is thereafter identified. The normal line direction indicatedby the polygon data correlated with the identified visible polygon 34 dis thereafter inverted. In this case, for example, the order of thesecond point ID and the third point ID is transposed, of the three pointIDs included in the vertex data of the polygon data.

As a result of sequentially deleting the polygons 34 constituting theinitial polygon model 40 depicted in FIG. 6, a polygon 34 whose normalline direction is not directed from the inner side toward the outer sideof the outer surface, of the polygon model may be present. For thepolygon 34, the normal line direction thereof is also corrected to bedirected from the inner side toward the outer side of the outer surface,of the polygon 34 by the normal line direction correction processdescribed above.

The final polygon model 30 exemplified in FIG. 3 is thereafter generatedby the execution of the invisible polygon deletion process and thenormal line direction correction process as above.

When the rendering function of the CPU is used, the virtual space image54 can be easily generated. In the present embodiment, the visiblepolygon 34 d is thereafter identified on the basis of the virtual spaceimage 54 capable of being easily generated as above and the invisiblepolygon can therefore be easily identified.

As described above, in the present embodiment, the highly precise finalpolygon model 30 copying the object 20 to be shot can be generated witha low processing load by the simple process of deleting the polygons 34from the initial polygon model 40 exemplified in FIG. 5.

The functions of the polygon model generating apparatus 10 according tothe present embodiment and the processes executed by the polygon modelgenerating apparatus 10 will further described below.

FIG. 13 is a functional block diagram depicting an example of thefunctions implemented in the polygon model generating apparatus 10according to the present embodiment. As depicted in FIG. 13, the polygonmodel generating apparatus 10 includes as its functions, for example,shot image storing part 60, a camera data storing part 62, a polygonmodel data storing part 64, a shot image obtaining part 66, a cameradata obtaining part 68, a point group data generating part 70, aninitial polygon model generating part 72, a point density valuedetermining part 74, a threshold value determining part 76, a long-sidepolygon deleting part 78, a corresponding camera position identifyingpart 80, an intersectional polygon deleting part 82, a visible attributesetting part 84, a virtual camera arranging part 86, a virtual spaceimage generating part 88, a visible polygon identifying part 90, anormal direction correcting part 92, and an invisible polygon deletingpart 94.

The shot image storing part 60, the camera data storing part 62, and thepolygon model data storing part 64 are implemented mainly in the storingpart 14. The shot image obtaining part 66, the camera data obtainingpart 68, the point group data generating part 70, the initial polygonmodel generating part 72, the point density value determining part 74,the threshold value determining part 76, the long-side polygon deletingpart 78, the corresponding camera position identifying part 80, theintersectional polygon deleting part 82, the visible attribute settingpart 84, the virtual camera arranging part 86, the virtual space imagegenerating part 88, the visible polygon identifying part 90, thermalline direction correcting part 92, and the invisible polygon deletingpart 94 are implemented mainly in the processor 12.

The above functions may also be implemented by execution by theprocessor 12 of a program installed in the polygon model generatingapparatus 10 that is a computer, and including orders that correspond tothe above functions. This program may be supplied to the polygon modelgenerating apparatus 10 through a computer-readable information storagemedium such as, for example, an optical disc, a magnetic disc, amagnetic tape, a magnetooptical disc, or a flash memory, or through theInternet or the like.

In the present embodiment, for example, the shot image storing part 60stores therein the one or plural shot images obtained by shooting theobject 20 to be shot, by the real camera 24 in the real space 22. Theshot image, storing part 60 may store therein a shot image that iscorrelated with the depth information such as a depth image.

In the present embodiment, for example, the camera data storing part 52stores therein camera data that indicates the position, the orientation,the angle of view, and the like of the real camera 24 in the real space22 at the time when the shot image is shot. In the case where the shotimage storing part 60 stores therein plural shot images, the camera datastoring part 62 stores therein plural pieces of camera data that arecorrelated with the shot images.

In the present embodiment, for example, the polygon model data storingpart 64 stoles therein the point group data that includes plural piecesof point data exemplified in FIG. 5, and the polygon model data thatincludes the plural pieces of polygon data exemplified in FIG. 7.

In the present embodiment, for example, the shot image obtaining part 66obtains the one or plural shot images stored in the shot image storingpart 60.

In the present embodiment, for example, the camera data obtaining part68 obtains the one or plural pieces of camera data stored in the cameradata storing part 62.

In the present embodiment, for example, the point group data generatingpart 70 generates the point group data on the basis of the shot imagesObtained by the shot image obtaining part 66 and the camera dataobtained by the camera data obtaining part 68, and causes the polygonmodel data storing part 64 to store therein the generated point groupdata.

In the present embodiment, for example, the initial polygon modelgenerating part 72 generates the initial polygon model 40 that includesthe plural polygons 34, on the basis of the point group data stored inthe polygon model data storing part 64. In this case, for example, theinitial polygon model 40 may be generated that includes the pluralpolygons 34 each having vertexes that are points 36 that belong to thegroup of points indicated by the point group data stored in the polygonmodel data storing part 64. In the present embodiment, for example, theinitial polygon model generating part 72 thereafter cause the polygonmodel data storing part 64 to store therein the generated initialpolygon model 40.

In the present embodiment, for example, the point density valuedetermining part 74 determines the value of the point density correlatedwith each of the points 36 that belong to the group of points as above,on the basis of the distribution of the group of points indicated by thepoint group data stored in the polygon model data storing part 64.

In the present embodiment, for example, for each of the polygons 34indicated by the polygon data stored in the polygon model data storingpart 64, the threshold value determining part 76 determines thethreshold value correlated with the side 42 that constitutes the polygon34 as above. In this case, the threshold value determining part 76 maybe adapted to determine a smaller value as the threshold valuecorrelated with the value of the point density as the value of the pointdensity is greater. The threshold value determining part 76 may retaindata that indicates the rule for the correlation between the value ofthe point density and the threshold value. The threshold valuedetermining part 76 may thereafter determine the threshold value usingthis data.

In the present embodiment, for example, in the case where the length ofthe side 42 constituting the polygon 34 exceeds the threshold valuecorresponding to the value of the point density correlated with the endpoint of the side 42, the long-side polygon deleting part 78 deletes thepolygon 34 from the polygon model. In this case, the long-side polygondeleting part 78 may delete the polygon 34 that includes the side 42whose length, is larger than the threshold value correlated thereto,from the polygon model as above. Moreover, the polygon data includingthe polygon ID of the polygon 34 that includes the side 42 whose lengthis larger than the threshold value correlated thereto may be deletedfrom the polygon model data.

In the present embodiment, for example, on the basis of the camera dataobtained by the camera data obtaining part 68, the corresponding camera,position identifying part 80 identifies the corresponding cameraposition that is the position in the virtual space 32 corresponding tothe position of the real camera 24 in the real space 22 indicated by thecamera data.

In the present embodiment, for example the intersectional polygondeleting part 82 identifies the polygon 34 that intersects with the linewhose, both ends are the position to view therefrom the polygon model inthe virtual space 32 and the position of the point 36 that belongs tothe group of points indicated by the point group data.

Concerning the above, the polygon 34 that intersects with a line whose,both ends are the corresponding camera position of the real camera 24and the point 36 corresponding to the surface of the object 20 to beshot whose image is included in the shot image shot by the real camera24 may be identified as above. Moreover, only each of at least some ofthe points 36 for which the value of the point density correlatedthereto is larger than a predetermined value, the polygon 34intersecting with the line whose both ends are the position of thispoint 36 and the position to view therefrom the polygon model in thevirtual space 32 may be identified.

Moreover, for example, in the virtual space 32, the polygon 34intersecting with a line whose both ends are the point of infinity forthe center of the polygon model and the point 36 may be identified.Moreover, for example polygon 34 intersecting the line whose both endsare the position that is distant from the center of the polygon model bya predetermined number-fold (such as, for example, a 1.5-fold or athree-fold) distance or longer of the radius of the sphere including thepolygon model and the point 36 may be identified.

Moreover, for example, the polygon 34 intersecting with the line whoseboth ends are the position to view therefrom the polygon model in thevirtual space 32 set by the user and the point 36 may be identified.

In the present embodiment, for example, the intersectional polygondeleting part 82 thereafter deletes the identified polygon 34 from thepolygon model. Concerning this, for example, the polygon data includingthe polygon ID of the identified polygon 34 may be deleted from thepolygon model data.

In the present embodiment, for example, the visible attribute settingpart 84 sets, in each of the polygons 34 constituting the intermediatepolygon model 50 arranged in the virtual space 32, the visible attributecorrelated with the polygon 34.

In the present embodiment, for example, the virtual camera arrangingpart 86 determines the position and the shooting direction of thevirtual camera 52 in the virtual space 32. Concerning this, for example,the virtual camera arranging part 86 may vary the position and theorientation of the virtual camera 52 in accordance with the operation onthe operation part 16 by the user. The virtual camera arranging part 86may thereafter determine the arrangement of the virtual camera 52 inaccordance with a determination operation by the user.

In the present embodiment, for example, the virtual space imagegenerating part 88 generates the virtual space image 54 that shows thescene obtained by viewing from the position of the virtual camera 52arranged by the virtual camera arranging part 86 in the shootingdirection of the virtual camera 52. Concerning this, for example, pluralvirtual space images 54 showing the scenes obtained by viewing from thepositions that differ from each other may be generated.

In the present embodiment, for example, the visible polygon identifyingpart 90 identifies the visible polygon 34 d that is visible from thevirtual camera 52 on the basis of the virtual space image 54.

In the present embodiment, for example, the normal line directioncorrecting part 92 executes the normal line direction correction processdescribed above for each of the visible polygons 34 d identified by thevisible polygon identifying part 90.

In the present embodiment, for example, the invisible polygon deletingpart 94 identifies the invisible polygons that are the invisiblepolygons 34 of the any of the one or plural virtual cameras 52 set inthe virtual space 32. In the present embodiment, for example, theinvisible polygon deleting part 94 thereafter deletes the identifiedinvisible polygons from the polygon model. Concerning this, for example,the polygon data including the polygon ID of the invisible polygon maybe deleted from the polygon model data. Moreover, the polygon datacorrelated with each of the polygons 34 that are not identified each asthe visible polygon 34 d in any of the virtual space images 54 may bedeleted from the polygon model data.

Concerning the above, an example of the flow of the processes executedby the polygon model generating apparatus 10 according to the presentembodiment will be described with reference to a flowchart exemplifiedin FIG. 14. In addition, in the following example of the processes, itis assumed that the visible polygon ID list that is empty when theprocesses are started is retained by the visible polygon identifyingpart 90.

The shot image obtaining part 66 first obtains the one or plural shotimages stored in the shot image storing part 60 (S101). The camera dataobtaining part 68 thereafter obtains the camera data correlated with theshot image obtained in the process denoted by S101 stored in the cameradata storing part 62 (S102). In this example of the processes, it is asthat the plural shot images are obtained in the process denoted by S101and the plural pieces of camera data correlated respectively with theshot images in the process denoted by S102 are obtained.

The point group data generating part 70 thereafter generates the pointgroup data that includes the plural pieces of point data and causes thepolygon model data storing part 64 to store therein the generated pointgroup data (S103). Concerning this, the point group data may begenerated on the basis of the shot images obtained in the processdenoted by S101. Otherwise, the point group data may be generated on thebasis of the shot images obtained in the process denoted by S101 and thecamera data obtained in the process denoted by S102.

The initial polygon model generating part 72 thereafter generates thepolygon model data of the initial polygon model 40 on the basis of thepoint group data stored in the process denoted by S103, and causes thepolygon model data storm part 64 to store therein the generated polygonmodel data (S104).

Such processes are thereafter executed as the long-side polygon deletionprocess (S105), the intersectional polygon deletion process (S106), andthe invisible polygon deletion process (S107) in this order, and thepolygon model data to be correlated with the final polygon model 30 isfinally generated.

An example of the flow of the long-side polygon deletion processexecuted by the polygon model generating apparatus 10 according to thepresent embodiment and denoted by S105 will be described below withreference to a flowchart exemplified in FIG. 15.

Based on the distribution of the group of points indicated by the pointgroup data stored in the process denoted by S103, for each of the points36 respectively corresponding to the plural pieces of point dataincluded in the point group data, the point density value determiningpart 74 first determines the value of the point density that correspondsto this point 36 (S201).

For each of the plural pieces of poly on data included in the polygonmodel data generated in the process denoted by S104, the threshold valuedetermining part 76 thereafter determines the threshold value that iscorrelated with the side 42 of the polygon 34 indicated by the polygondata (S202). Concerning this, for example, the side 42 corresponds to acombination of the points 36 that are respectively correlated with thetwo point IDs included in the vertex data of the polygon data. For thepoints 36 respectively correlated with these two point IDs, thethreshold value correlated with the side 42 can be determined on theoasis of the value of the point density determined in the processdenoted by S105.

The long-side polygon deleting part 78 thereafter identifies the polygon34 that includes the side 42 for which the length of the side 42 exceedsthe threshold value determined for the side 42, from the sides 42 forwhich the threshold value is determined in the process denoted by S202(S320).

The long-side polygon deleting part 78 thereafter deletes the polygondata that includes the polygon ID of the polygon 34 identified in theprocess denoted by S203, from the polygon model data stored in thepolygon model data storing part 64 (S204). The long-side polygondeletion process (S105) is thereafter caused to come to an end.

An example of the flow of the intersectional polygon deletion processexecuted by the polygon model generating apparatus 10 according to thepresent embodiment and denoted by S106 will be described below withreference to a flowchart exemplified in FIG. 16.

The corresponding camera position identifying part 80 first identifiesthe corresponding camera positions of the real camera 24 respectivelycorrelated with the pieces of camera data, based on the pieces of cameradata obtained in the process denoted by S102 (S301). Because the pluralpieces of camera data are obtained in this example of the process, theplural corresponding camera positions are identified.

The intersectional polygon deleting part 82 thereafter selects onecorresponding camera position for which none of the processes denoted byS303 to S307 below is executed, from the corresponding camera positionsidentified in the process denoted by S301 (S302).

The intersectional polygon deleting part 82 thereafter identifies theshot image shot by the real camera 24 whose position corresponds to thecorresponding camera position selected in the process denoted by S302(S303).

The intersectional polygon deleting part 82 thereafter identifies theplural points 36 corresponding to the surface of the object 20 to beshot whose image is included in the shot image identified in the processdenoted by S303 (S304).

The intersectional polygon deleting part 82 thereafter extracts thepoints 36 that are determined in the process denoted by S201 and forwhich the values of the point density correlated therewith are eachgreater than the predetermined value, from the plural point 36identified in the process denoted by S304 (S305).

For each of the plural points 36 extracted in the process denoted byS305, the intersectional polygon deleting part 82 thereafter identifiesthe polygon 34 that intersects with the line whose both ends are theposition of the point 36 and the corresponding camera position selectedin the process denoted by S301 (S306).

The intersectional polygon deleting part 82 thereafter deletes thepolygon data that includes the polygon ID of the polygon 34 identifiedin the process denoted by S306, from the polygon model data stored inthe polygon model data storing part 64 (S307).

The intersectional polygon deleting part 82 thereafter checks whetherany corresponding camera position that is not selected in the processdenoted by S302 and for which none of the processes denoted by S303 toS307 is executed is present (S308). In the case where the intersectionalpolygon deleting part 82 determines that such a corresponding cameraposition is present (S308: Y), the flow returns to the process denotedby S302. In the case where the intersectional polygon deleting part 82determines that no such corresponding camera position is present (S308:N), the intersectional polygon deletion process (S106) is caused to cometo an end.

An example of the flow of the invisible polygon deletion processexecuted by the polygon model generating apparatus 10 according to thepresent embodiment and denoted by S107 will be described below withreference to a flowchart exemplified in FIG. 17.

The visible attribute setting part 84 first sets the visible attributesthat differ from each other for each of the pieces of polygon dataincluded in the polygon model data stored in the polygon model datastoring part 64 (S401).

The virtual camera arranging part 86 thereafter determines the positionof the virtual camera 52 to view the polygon model in the virtual space32 and the shooting direction of the virtual camera 52 (S402).Concerning this, for example, the position and the shooting direct ionmay randomly be determined, or the position and the shooting directionmay be determined in accordance with the designation by the user.

The virtual space image generating part 88 thereafter generates thevirtual space image 54 that shows the scene obtained by viewing from theposition of the virtual camera 52 in the shooting direction of thevirtual camera 52 (S403).

The visible polygon identifying part 90 thereafter identifies thevisible polygons 34 d that are visible from the virtual camera 52 on thebasis of the virtual space image 54 generated in the process denoted byS403 (S404).

The visible polygon identifying part 90 thereafter adds the polygon Itsof the visible polygons 34 d identified in the process denoted by S404to the visible polygon ID list (S405). In addition, in this example ofthe process, it is assumed that, when the polygon Its are added to thevisible polygon ID list, the normal line inversion count value whoseinitial value is zero is correlated with each of the polygon IDs.

For each of the visible polygons 34 d identified in the process denotedby S120, the normal line direction correcting part 92 thereaftercalculates the value of the inner product of the vector V1 in theshooting direction of the virtual camera 52 and the vector V2 in thenormal line direction of the visible polygon 34 d (S406).

The normal line direction correcting part 92 thereafter updates thenormal line inversion count value that is correlated with the polygon IDincluded in the visible polygon ID list, in accordance with the value ofthe inner product calculated in the process denoted by S405 (S407).Concerning this, for example, the normal line in count value correlatedwith the polygon ID of the visible polygon 34 d whose calculated valueof its inner product is positive is increased by one. Moreover, thenormal line inversion count value correlated with the polygon ID of thevisible polygon 34 d whose calculated value of its inner product isnegative is reduced by one.

The invisible, polygon deleting part 94 thereafter checks whether or notthe processes denoted by S403 to S407 are repeatedly executed for thenumber of times determined in advance (S408). Concerning this, it isassumed that the invisible polygon deleting part 94 confirms that theprocesses are not yet repeatedly executed for the number of timesdetermined in advance (S408: N). In this case, the virtual cameraarranging part 86 varies the position of the virtual camera 52 to viewthe polygon model and the shooting direction of the virtual camera 52 inthe virtual space 32 (S409) and the flow returns to the process denotedby S403. Concerning this, the posit ion and the shooting direction mayrandomly be varied or may be varied to the position and the shootingdirection designated by the user.

It is assumed that, in the process denoted by S408, the invisiblepolygon deleting part 94 confirms that the processes are repeatedlyexecuted for the number of times determined in advance (S408: Y). Inthis case, the normal line direction correcting part 92 identifies thepolygon ID whose normal line inversion count value correlated thereto ispositive, from the polygon IDs included in the visible polygon ID listretained by the visible polygon identifying part 90 (S410).

The normal line, direction correcting part 92 thereafter inverts thenormal line direction indicated by the polygon data that includes thepolygon ID identified in the process denoted by S409 stored in thepolygon model data storing part 64 (S411). In the process denoted byS411, for example, the normal line direction correcting part 92transposes the order of the second point ID and the third point ID ofthe three point IDs included in the vertex data of the polygon data thatincludes the polygon ID identified in the process denoted by S410.

The invisible polygon deleting part 94 thereafter identifies theinvisible polygon on the basis of the visible polygon ID list retainedby the visible polygon identifying part 90 and the polygon data storedin the polygon model data storing part 64 (S412).

The invisible polygon deleting part 94 thereafter deletes the polygondata that includes the polygon ID of the invisible polygon identified inthe process denoted by S411, from the polygon model data stored in thepolygon model data storing part 64 (S413). The invisible polygondeletion process (S107) is thereafter caused to come to an end.

In addition, in the example of the processes depicted in FIG. 17, theprocesses denoted by S406, S407, S410, and S411 correspond to the normalline direction correction process described above.

In the example of the processes described above, for example, theintersectional polygon deletion process denoted by S106 may be executedwithout executing the long-side polygon deletion process denoted byS105. Moreover, instead of the long-side polygon deletion processdenoted by S105, a process of uniformly deleting the polygons 34 eachincluding the side 42 that is longer than the predetermined length maybe executed. Moreover, the long-side polygon deletion process denoted byS105 may be executed after executing the process of uniformly deletingthe polygons 34 each including the side 92 that is longer than thepredetermined length.

Moreover, the processes denoted by S306 and S307 may be executed for allthe points 36 that are identified in the process denoted by S304 withoutexecuting the process, denoted by S305.

Moreover, the processes denoted by S403 to S409 described above are notexecuted as the processes to be repeated, and plural sets of theposition of the virtual camera 52 and the shooting direction of thevirtual camera 52 may be adapted to be determined in the process denotedby S402 and the processes denoted by S403 to S407 may thereafter beexecuted in parallel processing.

Moreover, the invisible polygon deletion process denoted by S107 may beexecuted for the polygon model for which the long-side, polygon deletionprocess denoted by S105 and the intersectional polygon deletion processdenoted by S106 are not executed. Moreover, the invisible polygondeletion process denoted by S107 may not be executed after executing theintersectional polygon deletion process denoted by S106.

In addition, the present invention is not limited to the aboveembodiment.

Moreover, the above specific character strings and the above specificvalues, and the specific character strings and the specific values inthe drawings are exemplification and the present invention is notlimited to these character strings and values.

The invention claimed is:
 1. A polygon model generating apparatuscomprising: a polygon model generating part that generates a polygonmodel that includes plural polygons on a basis of point group dataindicating a group of points in a virtual space; a point density valuedetermining part that determines a value of a point density correlatedwith a point belonging to the group of points on a basis of adistribution of the group of points; and a long-side polygon deletingpart that, in a case where a length of a side constituting the polygonexceeds a threshold value in accordance with the value of the pointdensity correlated with an end point of the side, deletes the polygonfrom the polygon model.
 2. The polygon model generating apparatusaccording to claim 1, further comprising: an intersectional polygonidentifying part that identifies an intersectional polygon that is thepolygon intersecting with a line whose both ends are a first position toview therefrom the polygon model in the virtual space and a secondposition that is a position of a point belonging to the group of points;and an intersectional polygon deleting part that deletes theintersectional polygon from the polygon model.
 3. The polygon modelgenerating apparatus according to claim 2, further comprising: an imageobtaining part that obtains an image obtained by shooting an object tobe shot by a real camera in a real space; a point group data generatingpart that generates the point group data for which points belongingthereto each correspond to a point on the object to be shot in the realspace, on a basis of the image; and a corresponding camera positionidentifying part that identifies a position in the virtual space, thatcorresponds to a position in the real space of the real camera at a timewhen the object to be shot is shot, wherein the intersectional polygonidentifying part identifies the intersectional polygon using a positionidentified in the corresponding camera position identificationprocedure, as the first position.
 4. The polygon model generatingapparatus according to claim 2, wherein, for only each of at least someof points for which values of the point density correlated thereto areeach greater than a predetermined value, the intersectional polygonidentifying part identifies the intersectional polygon using a positionof the point as the second position.
 5. The polygon model generatingapparatus according to claim 1, further comprising: an invisible polygonidentifying part that identifies an invisible polygon that is thepolygon invisible to any of one or plural virtual cameras set in thevirtual space; and an invisible polygon deleting part that deletes theinvisible polygon from the polygon model.
 6. A polygon model generationmethod comprising: generating a polygon model that includes pluralpolygons on a basis of point group data indicating a group of points ina virtual space; determining a value of a point density correlated witha point belonging to the group of points on a basis of a distribution ofthe group of points; and, in a case where a length of a sideconstituting the polygon exceeds a threshold value in accordance withthe value of the point density correlated with an end point of the side,deleting the polygon from the polygon model.
 7. A non-transitorycomputer readable medium having stored thereon a program for a computer,comprising: by a polygon model generating part, generating a polygonmodel that includes plural polygons on a basis of point group dataindicating a group of points in a virtual space; by a point densityvalue determining part, determining a value of a point densitycorrelated with a point belonging to the group of points on a basis of adistribution of the group of points; and by a long-side polygon deletingpart, in a case where a length of a side constituting the polygonexceeds a threshold value in accordance with the value of the pointdensity correlated with an end point of the side, deleting the polygonfrom the polygon model.